The idea of using machines to solve mathematical problems
can be traced at least as far as the early 17th
century. Mathematicians who designed and
implemented calculators that were capable of
addition, subtraction, multiplication, and division
included Wilhelm Schickhard,
Blaise Pascal, and Gottfried
Leibnitz.

The first multi-purpose, i.e. programmable, computing
device was probably Charles Babbage's Difference Engine,
which was begun in 1823 but never completed. A more
ambitious machine
was the Analytical Engine. It was designed in 1842,
but unfortunately it also was only partially
completed by Babbage. Babbage was truly a man
ahead of his time: many historians think the major
reason he was unable to complete these projects
was the fact that the technology of the day was not
reliable enough. In spite of never building a
complete working machine, Babbage and his
colleagues, most notably Ada, Countess
of Lovelace, recognized
several important programming techniques, including
conditional branches, iterative loops and index
variables.

A machine inspired by Babbage's design was arguably
the first to be used in computational science. George
Scheutz read of the difference engine in 1833, and
along with
his son Edvard Scheutz began work on a smaller version.
By 1853 they had constructed a machine that could
process 15-digit numbers and calculate fourth-order
differences. Their machine won a gold medal at the
Exhibition of Paris in 1855, and later they sold it to the
Dudley Observatory in Albany, New York, which used it
to calculate the orbit of Mars.
One of the first commercial uses of mechanical
computers was by the US Census Bureau, which used
punch-card equipment designed by Herman Hollerith to
tabulate
data for the 1890 census. In 1911 Hollerith's company
merged with a competitor to found the corporation
which in 1924 became International Business Machines.